Multi crystal oscillator for self temperature compensation

ABSTRACT

A multi-crystal oscillator for self temperature compensation comprising three parallel connected oscillator elements each having substantially parabolic frequency temperature characteristics within a predetermined compensated temperature range. The three elements being chosen to have the effective turnover temperatures in lower temperature portion, middle temperature portion and higher temperature portion. The inductances of the elements of the lower and higher temperature portions are selected to be nearly identical and that of the middle temperature portion is selected higher than that of the other portions. The frequency temperature characteristics of the oscillator is so arranged to have less degradation in the compensated temperature range when the oscillation frequency is adjusted by varying the load capacitance.

United States Patent [191 Onoe et al. t

[11] 3,821,666 June 28, 1974 MULTI-CRYSTAL OSCILLATOR FOR SELFTEMPERATURE COMPENSATION [75] Inventors: Morio Onoe, Tokyo; KoichiHirama,

Chigasaki, both of Japan [73] Assignee: Toyo Tsushinki Kabushiki Kaisha(also known as Toyo Communication Equipment C0,, Ltd.), Kawasaki, Japan22 Filed: Mar. 30, 1973 211 App]. No.: 346,384

[30] Foreign Application Priority Data Apr. 3, 1972 Japan .l I. 47-33321[52] U.S. Cl 331/162, 331/167, 331/176 [51] Int. Cl. H03b 5/32 [58]Field of Search 331/116, 162, 167, 176

[56] References Cited FOREIGN PATENTS OR APPLICATIONS 959,927 3/1957Germany r; 331/162 Primary Examiner-John Kominski Attorney, Agent, orFirm-Sughrue, Rothwell, Mion, Zinn & Macpeak 57] ABSTRACT Theinductances of the elements of the lower and higher temperature portionsare selected to be nearly identical and that of the middle temperatureportion is selected higher than that of the other portions. Thefrequency temperature characteristics of the oscillator is so arrangedto have less degradation in the compensated temperature range when theoscillation frequency is adjusted by varying the load capacitance.

3 Claims, 18 Drawing Figures PATENTEUmza 1974 r 3 15 55 SHEET H UF 6PATENTEJUNZB ism SHEET 8 BF 6 the oscillation frequency.

'. Compensated temperature range I Frequency adjustable range v 1 1MULTI-CRYSTAL OSCILLATOR FOR SELF TEMPERATURE COMPENSATION I BACKGROUNDOF THE INVENTION 1. Field of the Invention The present invention relatesto .a multi-crystal oscillator for obtaining frequency temperaturecompensation. More especially, the present invention is concerned in atemperature compensating multi-crystal oscillator comprising threecrystal elements connected in parallel and each having substantiallyparabolic temperature frequency characteristic in a predeterminedcompensating temperature range. The invention particularly concerns forthe selection of equivalent inductance values of the three parallelcrystal elements in order that the compensation characteristic of theoscillator does not unduly deteriorate due to adjustment of 2.Description of the Prior Art The demand for crystal oscillators havingmedium degree of accuracy shows more and more increase according to thepopularization of frequency counters or high accuracytransceiver.

The major electric characteristics requested for such kind ofoscillators are listed in the following Table-l, in which 5 items are tobe taken into account.

TABLE l Item Standards Warm up time to bein the above standard valuejust after the switching on Power consumption as small as possible 'llheconventional oscillators are classified into two systems. The first oneis an oven system in which an oscillator is placed in an oven chamberand the oscillating frequency is stabilized by keeping the chambertemperature constant. The second one is a temperature compensationsystem using a temperature sensitive element associated with theoscillator element.

The first oven system has a serious drawback in that a considerable longtime is required beforethe oven chamber'arrives a required constanttemperature and only thereafter a specified frequency stabilization isobtained. Because of such delay-working, the oven system is not suitablefor use in an application in which immediate operation of apparatus isrequested after the switching on. Furthermore, this system requires apower for heating the oven after obtaining a specified frequencystability and suchdevice consumes even that various non-linear elements,such as variable caj the frequency adjustable range. This is due to afact pacitance semi-conductors or thermisters, are used in this systemand hence a small variation of the operating point by an adjustment ofthe frequency of the system may deteriorate to temperature compensationcharacteristic.

One temperature compensation system using 3 BT- cut crystals and anon-thermostat system had been disclosed along with calculatedembodiments in: D. J. Fewings et al., A Self Compensating CrystalOscillator, The Marconi Review, vol XXXI No. 169 Second Quarter 1968pp.57-78. The above oscillator is a temperature compensating systemusing three oscillating elements of identical equivalent inductance andhaving substantially parabolic frequency temperature characteristics andhaving nearly equalturnover temperature intervals and slightly shiftedturnover frequencies. The

disclosure just shows one general embodiment having a frequencystability of il-lX 10', and a compensated temperature range of 120Cobtained by calculation and did not refer to the realizationof thecircuit values.

However, in the above suggestion, due to nonproperdeterioration of thefrequency character, which will be explained further detail lateron,isconsiderable and as the resultthe third item of the Table-I, therequirement for the frequency adjustable range, is not fulfilled so thata practical device has never been realized.

This drawback will be explained in further detail hereinafter.

If we consider a case that three oscillator elements No. l, No. 2 andNo. 3 each having an identical inductance value and having frequencytemperature chracteristics as shown bycurves 1, 2 and 3 in FIG; 1 areconnected in parallel as-shown in FIG. 2 between terminals ll and 12 andare connected in series with a negative load resistance R and a loadcapacitance C so as to form an oscillator circuit having an equivalentload capacitance of C =C in this condition, then the composite frequencytemperature characteristic becomes as curve 4 of FIG. l, which shows. acompensated frequency temperature characteristic having less frequencyvariation in a certain compensationtemperature range.

By using the above idea, the first and second standards in Table-I canbe satisfied. However, if the load capacitance is to be adjusted as C =CMC in order to satisfy the third standard to vary the oscillatingfrequency, then the composite compensation curve varies as shown curves5, 6 and 7 of FIG. 3. This means that even at a certain load capacitanceof C the first and second items in Table-I had been satisfied forinstance as shown in curve6 of FIG. 3, the standards can no longer besatisfied 'by varying the operating frequency as shown by curves 5 and7.

SUY oF THE INVENTION The inventors considered that such change infrequency temperature characteristics by changing the 1 operatingfrequency is mainlycaused by a fact that the frequency sensitivity forthe load capacitance by middle temperature portion of a compensatingrange is larger than that of higher or lower temperature portion afterobserving the characteristics shown in FIG. 3.

j The-present invention has for its object to mitigate above-mentioneddisadvantage of the conventional oscillator and to obtain a practicalmulti-cryst'al oscillator having satisfactory temperature compensatingcharacteristics fora desired range of adjusting frequencies.

The present inventionhas been obtained by a consideration of a fact thatby choosing the equivalent inductance of the middle temperature portionto be higher BRIEF DESCRIPTION OF THE DRAWINGS The principle of thepresent invention will become more clear by the following descriptionreferring to the accompanied drawings, in which:

FIG. 1 shows frequency temperature characteristic curves of threeoscillating elements individually and that for a combination thereof; Il FIG. 2 shows a typical circuit for three elements multi-crystaloscillator; I

FIG. 3 shows frequency temperature characteristic curves of aconventional multi-crystal oscillator illustrating the fact thatrequirements are not fulfiled by frequency adjusting;

FIG. 4 shows an example of the frequency tempera-' ture characteristiccurves, of a multi-crystal oscillator made accordance with the principleof the present invention having higher equivalent inductance in themedium temperatureportion to obtain a good frequency temperaturecharacteristics;

' FIG. 5 is a frequency temperature characteristic curves in which thesecond-order coefficient is negative;

FIG. 6 is an illustrative frequency temperature characteristics inwhich'the second-order coefficient is posime;

FIGS. 7a to 7e are equivalent circuit diagrams for explaining thepresent invention;

. FIG. 8 is a graph showing one solution of the frequency formula; I

FIG. 9 is a graph illustrating the relation between equivalentinductance ratio a and normalized total-reactance B and also normalizedturnover frequency separation D when the frequency temperaturecharacteristics show equal ripple characteristics;

FIG. l0is a graph for explaining definition of normalized frequencydeviation AD and normalized'tempera ture compensating range AT;

FIG. 11 is a graph showing relation between figure of merit I B and a;

FIG. 12 is a graph for explaining degradation factor FIG. 13 showsrelation between B, (I) and a; and FIG. 14 shows relation between 1' anda.

I DESCRIPTION OF THE PREFERRED EMBODIMENT The principle of the presentinvention will be explained by referring to the accompanied drawings.

FIG. 4 shows one example of frequency temperature characteristicsobtainable in accordance with the present invention. In FIG. 4 curves 8,9 and show the cases when the respective load capacitance C is changedas C =C tAC As can be seenfrom the 4 curves 8, 9 and 10, the maximumpoints in respective curves show substantially parallel displacement inorder to satisfy the first and second requirements in Table-I even whenthe operating frequency is adjusted in a range of the third requirement.

In the above-mentioned D. .l. Fewings suggestion, three oscillationelements each having identical equivalent inductance are used. But theinventors had realized a fact that a practical oscillator having a widefrequency adjusting range and having a temperature compensatingcharacteristic of less degradation, which will be explained in moredetail lateron, can only be realized by selecting the equivalentinductance of the middle temperature portion to be larger than theequivalent inductance of the higher or lower temperature I portion beingselected to have an identical value.

The idea of temperature compensation will be explained. At firsttheoretical analysis of the oscillator of the present invention based onseveral assumptions will be explained and then the reason for providingsuch assumption will be explained. The following analysis based onseveral hypothetical assumptions will give nearly complete natures ofthe temperature compensation characteristic of an oscillator system madein accordance with the present invention. The inventors had confirmed byactual experiments and by precise calculations based on formulae derivedin the present invention that practical oscillators operating withoutsuch assumptions show fairly good temperature compensa tion effect andhaving substantially the same frequency temperature characteristics withthat obtained by the theoretical analysis under the hypotheticalassumptions.

The following four assumptions were introduced.

1. The loss of an oscillator element is neglected in view of its high Qvalue.

2. The frequency temperature characteristic of an oscillator element isassumed to be a parabolic form and its second-order coefficient isassumed to be identical for the three oscillator elements.

3. No deviation of characteristic exists for the products at themanufacturing and it can be made in sufficient approximation to thepredetermined values.

4. Unless particularly mentioned, all the parameters are assumed to haveno temperature depending characteristics.

The three parallel connected oscillator elements No. 1, No. 2 and No. 3,which might be referred also as lower temperature portion, middletemperature portion and higher temperature portion, respectively, haveeach temperature characteristic of the series resonant angular frequencyin parabolic form as shown by curves 1, 2 and 3 in FIG. 5. The abscissaof the graph of FIG. 5 is temperature t and the ordinate of the same isthe angular frequency w. The three parabolic curves 1, 2 and 3 showtemperature characteristics of the series resonant angular frequencies(03 (0 and (.0 of the three oscillator elements No. 1, No. 2 and No. 3.The turnover temperatures t' t' and t of the curves 1, 2

. and 3 in FIG. 5 are chosen to have identical intervals.

By the assumption that the second-order coefficients of the threeoscillator elements are identical to be a,

the relation between the series resonant angular frequency m and thetemperature I, of the oscillator elements of FIG. 5 becomes as follows.

3 In the following explanation use is made a temperature t, which is atemperature deviating from the temperature t (t'= t+t' Also popularlyused idea of frequency deviation for the angular frequency isintroduced. In this particular definition, series resonant frequencydeviation 8,, means a ratio of deviating frequency from the turnoverangular frequency am under consideration.

The series resonant frequencydeviation 8,, can be expressed by thefollowings.

A turnover frequency separation 8 is defined by the following formulawith respect to the difference between the turnover angular frequency wof the middle temperature portion and the other mutually identicalturnover angular frequencies (o and m 5 The second-order coefficient a,when using the frequency deviation, is termed by the following.

. 6 The following relations are obtained by using formulae (3) and (I),(2), (4), (5) and (6).

FIG. 6 is a diagram illustrating above relation.

In FIG. 6, the ordinate represents the frequency deviation 8 deviatingfrom the turnover angular frequency (0 0f the oscillator element No. l,which is now located at the origin, and the abscissa representstemperature t making the turnover temperature 1' of the oscillatorelement No. 2 as the origin.

In FIG. 5, the characteristic curves are illustrated as convex curvessince practical quartz oscillator elements having parabolic shapedfrequency temperature tor portion is as shown in FIG. 7a by assuming nocircuit loss is included. As shown in FIG. 7a, equivalent inductances inthe series arms of the three oscillators No. I, No. 2 and No. 3 arerepresented by L L and L respectively. Equivalent capacitance in therespective series arms are represented by C C and C and the parallelcapacitances are represented by C C and C respectively. We may assumethat the temperature dependent variation of the series resonant angularfrequency is caused by temperature dependent variation of the equivalentcapacitance in the series arm of the equivalent circuit of eachoscillator element.

The. equivalent circuit of FIG. 7a, may be modified as shown in FIG. 7b.In the oscillator circuit shown in the down side of FIG. 2, betweenterminals 111 and 12, the load resistance R, can be made as zero ifconsidering to drive the oscillator elements having no loss so that theequivalent circuit becomes as shown in FIG. 7c. By connecting theequivalent circuit for the oscillator element portion shown in in FIG.7b and that for oscillating circuit shown in FIG. in series, then anequivalent circuit shown in FIG. 7d can be obtained. In this circuit,the oscillating frequency may be decided under a condition that thereactance between the terminals 19 and 211 being zero. This condition isjust same as a condition of reactance between terminals 22 and 24becomes zero in a modified equivalentcircuit as shown in FIG. 7e. Thefollowing explanation will be given by referring to thus modifiedequivalent circuit diagram as shown in FIG. 7e. By using thus modifiedequivalent circuit diagram as shown in FIG. 72, the analysis can be madeeasier since we can consider the analysis by separately considering intotwo portions, i.e., a parallel connected portion of the three seriesarms of the three oscillator elements between the terminals 22 and 23and a capacitance portion formed by a sum of the load capacitance C andthree parallel capacitances C C and C as connected between terminals 23and 24.

At first we may consider the frequency characteristics of the reactancebetween the terminals 22 and 23 of FIG. 7e. The three series resonantangular frequencies may be written by the following formula by usingsubindexes shown in FIG. 7e.

I By defining respective reactances of each of the series arms as X thefollowing relation can be obtained, wherein w is angular frequency nearthe series resonant point.

Just in the same manner as has been done in the equation (4), we maydefine frequency deviation 8; for

an angular frequency w deviating from each series resonant angularfrequency to, of the respective oscillator element.

10 In the followings our consideration is based upon the frequencydeviation as mentioned in the formulae (4), (5) and (10).

The formula (9) can be modified by using formulae 8 and 10 as follows.

The inventors suggest to settle the equivalent reactances L L and L ofthe three oscillator elements No. 1 (lower temperature portion), No. 2(middle temperature portion) and No. 3 (higher temperature portion) asfollows:

Ln L

L 2 (XL 13 Wherein 6 is a constant larger than 1 and L is a standardvalueof inductance. In accordance with the present invention, theequivalent inductance of the middle temperature portion is selected 01times of the equivalent inductances L of the lower and highertemperature portion which are identical with each other.

The following relation can be obtained by introducing equations (13)into equation (12) for each item.

X2 ai aL26 l4 Wherein 5 is the frequency deviation of frequency w fromthe series resonant angular frequency a) The three series resonantangular frequencies (a deffer the value slightly with each other. Thevalue thereof may vary according to the temperature according toequation (7). However, as the difference of values and variations arevery small so that, as far as in the range to be considered, we mayassume the following relation without causing practical inaccuracy.

15 wherein, (o to is the turnover angular frequency of the element No. land is a constantfFurthermore the difference between ru and (o is smallso that we may assume these are equal.

The right termof equation (10) is modified to be expressed by frequencydeviation from (o as follows.

8, (ti-w lru When considering equation (15):

, I 17 Then by equation (4), the following relation establishes.

Wherein 6 is the frequency deviation of an angular frequency w deviatingfrom the turnover angular frequency ca of the oscillator element No. 1.This value 8 is chosen as the ordinate of the graph of FIG. 6 and isdefined by the following formula.

5 w-um/m 19 In the equation l4), 8, is frequency deviation 6 of anangular frequency w deviating from the turnover an gular frequency (o ofthe oscillator element No. 1 and subtracted by the specific frequency8,,- of the series resonant angular frequency 8 Namely 8 representsreactance X,- of the oscillator element in equation 14) by frequencydeviation 5 based on arbitrarily selected frequency and temperature I.

Then the reactance X of the parallel connected series arms between theterminals 22 and 23 of FIG. 72

may be expressed by using reactance X of the respective series arm asfollows.

Then by introducing equation (7) into (18), and

(l5), (18) into (14) and, in turn (14) into (20) and after rearrangingthe factor with respect to the frequency deviation 6;

T z/r D 8/0002 In the above formulae, the terms T, D, D B are normalizedtemperature, normalized frequency deviation, normalized turnoverfrequency separation, and normalized total reactance, respectively.

The above formulae of (21) and (22) will give oscillation frequency ofthe multi-crystal oscillator, when the reactance between terminals 22and 23 of FIG. 7e is X represented by normalized frequency deviation D.The equation is ternary equation with respect to the normalizedfrequency deviation D and must have three real roots when the loss ofother oscillator elements is assumed as zero as is the analysis of thepresent case.

Among the three real roots, only one root having minimum value has thetemperature compensation effect of the frequency. In practice, as thepractical oscillator element contains. loss and hence the oscillation ispossible only by the one real root.

The formulae (2]) and (22) can be written as follows.

F(D, T, D B, a) O The above equation may be considered to representrelation between the normalized frequency deviation D and the normalizedtemperature T having parameters of normalized turnover frequencyseparation D normalized total reactance B and equivalent inductanceratio or.

Hereinafter, the necessary condition of the present invention will beexplained. As the first necessary condition (i) the relation between,the normalized tumover frequency separation D normalized total reactanceB, and equivalent inductance ratio a is considered. Then as theessential feature of the present invention, (ii) the relation betweenvarious parameters which realizing parallel movement of the frequencytemperature characteristics parallel with frequency axis, at a minorchange of oscillation frequency is taken into consideration.

At first equal ripple characteristics may be considered. FIG. 8 showsone example of numerical solution offrequency equations shown informulae 21 and 22. In FIG. 8, the ordinate is chosen to be normalizedfrequency deviation D and the abscissa ischosen to be normalizedtemperature T. This figure shows only the minimum root of the normalizedfrequency deviation D which provides (temperature compensating effectfor the frequency. Furthermore, as the frequency temperaturecompensation characteristic curve is symmetrical with the ordinate, thenormalized temperature axis, only the positive portion of the curve isshown.

The conditions for obtaining numerical solution are that the normalizedoverall reactance B= 0.45, equivalent inductance ratio a=1. Threefrequency temperature characteristics curves shown in FIG. 8correspond-to each of the cases of normalized turnover frequencyseparation of the turnover point of the middle temperature portion being0.23, 0.24 and 0.25.

As can be seen from FIG. 8, in case the normalized turnover frequencyseparation of the middle temperature portion D is 0.24, the frequencytemperature characteristic shows equal ripple characteristics, whichmeans that the normalized frequency deviation D on the curve 050.24 hastwo minimum points of an identical value as shown by chain line. Thiscondition is the optimum condition being desired at temperaturecompensation for the frequency deviation over the wide temperaturerange.

FIG. 9 shows one numerical example for the normalized turnover frequencyseparation D for a given total reactance B under condition that-thefrequency temperature characteristics show equal ripple characteristics,and that the equivalent inductance ratio a is fixed under practicalrange of the various parameters.

In FIG. 9, ordinate is normalized turnover frequency separation D,abscissais normalized total reactance B and the parameters are selecteda ==l, (Jr-=2, (F4 and a==8. For the cases in which a has differentvalue from, above the obtained characteristic curves show equal ripplecharacteristics and also in these cases, normalized total reactance B ornormalized turnover frequency separation D, can be calculated.

One numerical example for the relation between the normalized turnoverfrequency separation D equivalent inductance ratio a and normalizedtotal reactance B showing equal ripple characteristics in the frequencytemperature characteristics had been obtained as shown by FIG. 9.

Then a figure of merit I, a quantity for showing the quality of theequal ripple characteristics may be considered.

As for quantities for defining the equal ripple characteristics, thefollowing two factors are defined, i.e., variation of the normalizedfrequency deviation AD and normalized compensation temperature range ATby using FIG. 10. In FIG. 110, the ordinate is chosen to be thenormalized frequency deviation D, and the abscissa is the normalizedtemperature T. The points a and c are the two minimum points having thenormalized frequency deviation D 'and D D respectively. The point b inFIG. 10 represents maximum point of the concave portion of the curvehaving the normalized frequency deviation D A point d having equalnormalized frequency deviation with that of the point b is settled onthe curve as shown in FIG. 10. The normalized temperature of point d isillustrated by T,,. The variation of the normalized frequency deviationAD and normalized temperature compensation range AT may be defined bythe following formulae.

In the present invention, a figure of merit I for the evaluationquantity 0 equal ripple characteristics by using said two factors of thevariation of the normalized frequency deviation AD and the normalizedcompensation temperature range AT is defined by the, following formula.

This figure of merit I has been defined by considering not only thefrequency variation but for the compensation temperature range. Theformula (26) has no higher order term, but by using the equation, thepractical degree of the compensation characteristics can easily beestimated. As can be seen from formula (26), the compensationcharacteristic becomes better according to the increase of the figure ofmerit However, according to the increase of this figure of merit I, theelements of oscillator becomes difficult to realize. As can be seen fromFIG. II, the normalized total reactance B must be negative and must havea large absolute value for obtaining a large figure of merit I, when theequivalent inductance ratio a is constant.

. In case of a quartz oscillator having parabolic frequency temperaturecharacteristics, the second-order coefficient is negative so that fromthe formula (23), the combined reactance X i.e., the reactance betweenterminals 22 and 23 of FIG. 7e becomes inductive. In order to make theresultant reactance between terminals 22 and 24 of FIG. 7e to be zero,the reactance between terminals 23 and 24 of FIG. 7e must be capacitiveand must have its absolute value equal to X Said later reactanceconsists of sum of the load capacitance C and three parallelcapacitances C C and C which sum is termed hereinafter as total parallelcapacitance.

In this connection if an equivalent inductance is given the parallelcapacitances C C and C become definite values so that only the loadcapacitance C can be varied at will. Therefore, if the figure of merit Ishould be made larger, the total parallel capacitance becomes smallerand accordingly the load capacitance C becomes smaller. In such case, asis usual for the normal quartz crystal oscillator, the oscillationbecomes impossible due to an increase of the effective resistance. If wechoose an extremely large figure of merit I, the total parallelcapacitance must have a value smaller than the sum value of the parallelcapacitances and the load capacitance must have a negative value so thatpractical element can not be realized.

By deciding equivalent inductance ratio or and normalized totalreactance B and by settling the normalized turnover frequency deviationD to'have equal ripple characteristics as shown in FIG. 9, thecorresponding normalized variation of frequency deviation AD and thenormalized compensation temperature range AT, and now the figure ofmerit I can be obtained from equation (26). In other words, if theequivalent inductance ratio a and the normalized total reactance B aredecided,.a corresponding figure of merit I is decided.

FIG. 11 shows one numerical embodiment showing the relation between thefigure of merit I and normalized total reactance B, in which theordinate is the figure of merit I, the abscissa is normalized totalreactance B and the parameter is the equivalent inductance ratio a.

From FIG. 11, it can be seen that there are a indefi nite number ofcombinations of the equivalent inductance ratio a and the normalizedtotal reactance B for giving a certain figure of merit I. Namely, for acertain figure of merit which will give, as an optimum temperaturecompensation of frequency temperature characteristics of the invention,the equal ripple characteristics, the equivalent inductance ratio a andthe normalized' total reactance B can be chosen considerably freelybased on FIG. 11. However, in order to satisfy less degradation whichforms the main subject of the present invention, there will be no suchfreedom for choosing the equivalent inductance ratio a and thenormalized total reactance B and the both quantities must have definitevalues. Hereinafter, the equivalent inductance ratio may be taken intoconsideration, which isa conveniently considered quantity for practicaldesign of a temperature compensating multi-crystal oscillator among twonecessary factors of the equivalent inductance ratio a and thenormalized total reactance B in order to realize not only the equalripple characteristics but for satisfying the requirement of lessdegradation".

In the usual requirement for such kind of an oscillator, the frequencyadjustable range is defined for instance as shown in the Table-I, item3. This requirement means that the oscillator satisfies both therequirements for the frequency deviation and the compensated temperaturerange when the oscillating frequency is adjusted in a range specified inthe Table-I.

This requirement has been defined based on a consideration that if theinitial temperature compensation characteristics were greatly distortedat other frequencies as shown by the curves and 7 of FIG. 3 when afrequency drift which may be due to aging at a certain frequency isadjusted, then the effect of temperature compensation is lost and thedevice becomes unpractical. Accordingly a function that the temperaturecompensation curve moves parallel to the direction of frequency axis isrequested when the oscillationfrequency is slightly adjusted. Inpractice it is frequent that such parallel movement is not attained.

As an amount to evaluate such irregulamess degradation factor is definedwhich will be explained by referring to FIG. 12. It is assumed thatcurve y in FIG. 12 has equal ripple characteristics at a normalizedtotal reactance B=B when the equivalent inductance ratio a and theturnover frequency separation D are given for instance such as shown inFIG. 8. The frequencies of two minimum points are D,, and Drespectively. The other curve 31 in FIG. 12 is made almost under sameconditions as the curve y except the fact that only the normalized totalreactance is slightly varied to be B B +AB. The frequencies of the twominimum points in this case is D, and D Then the degradation factor (1)is defined by the following formula.

d c c/ a a 1 FIG. 13 is a numerical example showing the relation betweenthe degradation factor (b and normalized total reactance B, in which theequivalent inductance a is chosen to be the parameter. The ordinate isdegradation factor (b and the abscissa is normalized total reactance B,wherein an increment AB of the normalized total reactance B is chosen tobe 0.005. This increment AB of 0.005 is selected by a reason that it isan amount sufficiently small with respect to the amount of B underconsideration and is a value sufficiently large to obtain desiredcalculation accuracy.

As can be understood by the equation (27), the compensation curve showsmovement nearer the parallel movement as the degradation factor (1)becomes nearer to zero. Referring to FIG. 13, :1) shows a value that4P0, when 0z=2 and B= O.38. In this case the parallel movementrequirement is satisfied at a small varia tion of B. This operatingpoint should be chosen under the following condition. The degradationfactor" Q5 is expanded as follows under a given normalized totalreactance B At the above operation point, in which oz=2 and B=O.38,according to the equation, the zero order term has value zero, but itsfirst order term has a considerably large value. Accordingly, if a widefrequency adjusting range is desired, an operating point should bechosen in which up to more higher order terms become zero. Such pointsmay be chosen in FIG. 13 so that the equivalent inductance ratio a is acertain curve, in which the degradation factor (I) is small and that thecurve is substantially parallel to the abscissa. In the illustratedembodiment, the operating points may be chosen on curve a=4 at portionabout B=0.8 to 0.9.

In the foregoing, it has been describedthat according to the main objectof the present invention, a characteristic for satisfying parallelmoving characteristics and having as the optimum compensationcharacteris- FIGS. 13 and 11 are the numerical embodiments calculated bymaking the degradation factor (b and normalizedtotal reactance B asindependent variables and by taking the equivalent inductance ratio a asthe parameter. FIG. 14 shows one numerical embodiment for the relationbetween the degradation factor (I) and the figure of merit I by makingthe equivalent inductance ratio oz as the parameter, which relation hasbeen obtained by using above two relations shown in FIGS. 13 and 11after eliminating the normalized total reactance B'therefrom. In FIG.14, the ordinate is the degradation factor 1b and the abscissa is thefigure of merit I.

It may be seen from FIG. 14 that an equivalent inductance ratio a whichshould bring the degradation factor (I) close to zero is determined if acertain figure of merit I corresponding to a desiredtemperaturecompensation is given. I

When a figure of merit I for an oscillator of medium grade is requiredto obtain under a given standard of frequency deviation and compensatedtemperature range as described in Table-I and then three crystaloscillator elements are used for three oscillators, the second-ordercoefficient a of frequency-temperature characteristic lies around therange of 29 so that from Table-l and equations 23 and 26, the figure ofmerit I should be limited to the following range.

In more detail, this means that values of I for a composite oscillatorconsisting of three elements are restricted to the condition of equation(30) as a result of exclusion of such cases that according to equation(26) the condition of 1,000 I must be fulfiled for the purpose ofproportioning the values of width AD between D and D, and the value ofAT within practical ranges and that any element having a value of I lessthan 20 can be realized even by a single oscillator.

Moreover, in practice, it is desired that the value of the degradationfactor (I) should be chosen within a following range.

As alsoseen from FIG. 14, this is based on a fact that the absolutevalue of the degradation factor I should be maintained small againstvarious values of I. This limit is considered under condition that evenif the oscillator frequency is deviated 20 times of AD of FIG. 10, whichsatisfies the equal ripple characteristics, the degradation, of thecompensation characteristic should be maintained at a degree that theequal ripple characteristicsis not unduly deteriorated in practice.

From these two conditional equations 30) and (3 l the equivalentinductance ratio a according to the invention is chosen to fulfil Suchlimitation is imposed due to the fact, as sho in FIG. 14, that the curvefor or=1 is located substantially outside the range of Il 0.05.

That is to say, a temperature compensation characteristic having equalripple characteristics is achieved by selecting the equivalentinductance of the middle temperature portion larger than those of thehigher and lower temperature portions which are equal each other.Moreover, such characteristic which is the principal object of theinvention and that the compensation curves are shifted in parallel tothe direction of the axis of frequency at slight change of frequencyoccurs can be provided under the same selection.

The equation (32) may be rewritten by the aid of equation (13) asfollows:

n ia l2 ll 1 Upon actual manufacturing it is impossible to realizevalues of these inductances to exactly coincide with those obtained bycalculation. However, as will be explained lateron, if the followingrelations between the equivalent inductances L L and L of the threeoscillator elements l2 ll 1 34 are realized by slightly adjusting thefrequencies and the effective turnover temperatures of the threeelements, it is possible by changing the load capacitance to providesuch characteristic that a frequencytemperature characteristic curve isshifted substantially in parallel within the range of temperaturecompensation.

Now, the basis of the assumptions previously mentioned will be reviewedand reconsidered.

Firstly, assuming that the oscillator elements used have high values of0, their loss is omitted. The practical elements such as crystaloscillators have Q-values of several ten thousands, resulting in verysmall loss. Therefore, said assumption is considered to have noinfluence.

Otherwise, existence of roots which is previously put out ofconsideration is reviewed. The frequency equations (21) and (22)resulting from omission of loss always have three real roots. However,taking account of I loss there are two cases of one real root and threereal roots (including the case of a real root and a double root). In thecase of one real root it is apparent from numerical calculation and/orexperiment taken account of loss that this root corresponds to thatprovides temperature compensation effect expressed in equation 21) and(22). Moreover, in the case of three real roots, equivalent resistancesof the three roots are finite and their respective values are generallyunequal. By numerical calculation and/or experiment with consid erationof loss it is foundthat an equivalent resistance which corresponds to aroot providing the temperature compensation effect defined in equations(21) and (22) is minimum. Accordingly, oscillation is rendered at afrequency corresponding to a root, which provides temperaturecompensation effect, among roots of equations (21) and (22).

Secondly, the frequency-temperature characteristics of the oscillatorsthemselves were in parabolic shape and all of their three second-ordercoefficients were equal. In practice, it is well known that BT or DT-cutoscillator elements of crystal have frequencytemperature characteristicsuch that it can be approxilator elements.

mated considerably well by a parabolic curve and its turnovertemperature can be varied over considerably wide range of temperature bychanging the cut-angle of the crystal. Under these circumstances asecond-order coefficient which is obtained in the above-mentioned mannerand defined by approximating the frequencytemperature characteristic toa parabolic curve within the temperature compensation range is referredto as an effective second-order coefficient. When the tumovertemperature exists within the range used according to the invention, theeffective second-order coefficient may be considered to be substantiallyconstant.

Similarly, a turnover temperature and a turnover frequency defined byapproximating a corresponding frequency-temperature characteristic to aparabolic curve are called as an effective turnover temperature and aneffectiveturnover angular frequency, respectively. According to theinvention, such effective values are used for all of various valuesstated previously.

Thirdly, dispersion or inhomogeneity upon manufacturing is reviewed.First of all, it is well known that inhomogeneous series resonantangular frequencies of the three oscillator elements can be broughtsufficiently close to desired values by connecting respective elementsof considerably small reactive values in series with each of theoscillator elements. In this case, variation of the equivalentinductance occurs simultaneously, however, such variation in value ofthe equivalent inductance caused upon adjusting dispersion in frequencyof the oscillator elements manufactured in conventional manner is verysmall, and hence can be neglected. Both of dispersion in the equivalentinductance and effective turnover temperature and slight difference inthe effective second-order coefficient act so asto deviate thefrequency-temperature characteristic from its symmetrical form withrespect to the frequency-axis, or deviate from equal ripplecharacteristics. However, characteristic curves close to ideal ones canbe obtained by slightly adjusting the frequencies and effective turnovertemperatures of the three oscillator elements.

As far as the degradation to which the invention is directed issatisfied, dispersion in parallel capacitances of respective oscillatorelements made by conventional way gives rise no problems.

' Moreover, we have assumed that the various parameters of constructiveelements for instance, the capacitances C C C etc. shown in FIG. 7e,have no temperature depending characteristics. However, even iftemperature variation of such factors apart from the series resonantangular frequency taken into account in the aforesaid analysis isconsidered, it acts to somewhat deviate symmetry of the temperaturecompensation characteristic curve with reference to its frequency axisor deviate equal ripple characteristics. However, such deviation ofcharacteristics from ideal form is very minor and in practice can bebrought close approximation to the ideal ones by slightly adjustingfrequencies and effective turnover temperatures of the three oscil-Consequently, even if some of the assumptions made 1 previously is notattained, characteristics, which are close to an ideal characteristic,i.e., equal ripple characteristics and less degradation, can be attainedby adjusting effective turnover temperatures of respective oscillatorelements and reactances connected in series with respective oscillatorelements.

In the foregoing, the invention has been explained with respect toconditions on which equal ripple characteristics that is ideal and mostuseful characteristic is improved. However, it is additionally statedthat even though there exists any incoincidence with equal ripplecharacteristics, such characteristics that a temperature compensationcharacteristic curve is shifted in parallel within the range oftemperature compensation can be attained by choosing the equivalentinductance ratio a greater than unity.

Manner of changing the equivalent inductance values of the oscillatorelements will be explained hereinbelow. It is well known that a value ofequivalent inductance can be varied in piezoelectric oscillator elementsby changing dimensions of electrodes attached thereto and especially, incontour oscillators over wide range by changing thickness ofpiezoelectric plate.

Now, the inventor proposes a method for changing values of effectiveequivalent inductances by connecting elements of considerably highreactance in series with the oscillator elements. According to thismethod, oscillator elements which are easily manufactured and havesubstantially equal equivalent inductances may be used to construct thetemperature compensated composite oscillator of the invention.

In this method, the frequency also varies simultaneously. However, suchincrements of frequency are predictable, so that pre-adjustment of thefrequency of the oscillator element itself to such value that saidincrements were subtracted does not need any additional process uponmanufacturing.

Also, in this case, dispersion in frequency of the oscillator elementscan be adjusted by means of said additional reactive elements forchanging the value of equivalent inductance.

According to the present invention, as it is possible to obtain amulti-crystal oscillator comprising three parallel connected oscillatorelements of which middle temperature element is so designed to have alarger inductance value and by merely adjusting the adjustable portionthereof the oscillator can be made operative in a predeterminedadjustable frequency range under a given compensating temperature rangeand frequency deviation, and being operable substantially simultaneouswith switching on and without power consumption. The present inventionis particularly effective for stabilizing oscillators for use frequencycounters, high accuracy transceiver, etc.

Various modifications might be possible without departing from the scopeof the present invention.

What is claimed is:

1. A multi-crystal oscillator for self temperature compensationcomprising three parallel connected oscillator elements each havingsubstantially parabolic frequency temperature characteristics within apredetermined compensated temperature range, the invention consists inthat effective turnover temperaturesof said three oscillator elementsbeing chosen to be lower temperature portion, middle temperature portionand higher temperature portion and that values of equivalent inductancesof said three elemtns L11, L1 and L are chosen according to thefollowing 3 formulae;

0.05 (b 0.05 wherein, the figure of merit I is given by,

l (ATV/AD and the degradation factor (I) is given by,

d) D /D -D,,- 1

wherein, AD represents variation of normalized frequency deviation at afrequency temperature characteristic having two minimum points of equaloscillation frequency and AD is difference of normalized frequencydeviation between the minimum frequency point and most deviatedfrequency point in a desired compensated temperature range,

AT is a normalized compensation temperature range corresponding to halfof the desired compensated temperature range,

D and D are normalized frequency deviations of the two minimum pointshaving identical value at the equal ripple characteristics,

D and D are normalized frequency deviations of corresponding points withsaid two points when oscillation frequency of the oscillator isadjusted.

l l= =l

1. A multi-crystal oscillator for self temperature compensationcomprising three parallel connected oscillator elements each havingsubstantially parabolic frequency temperature characteristics within apredetermined compensated temperature range, the invention consists inthat effective turnover temperatures of said three oscillator elementsbeing chosen to be lower temperature portion, middle temperature portionand higher temperature portion and that values of equivalent inductancesof said three elemtns L11, L12 and L13 are chosen according to thefollowing 3 formulae; L11 about L13 1 L12/L11 < 1 2 L12/L13 < 1 3 sothat frequency temperature characteristic curve of the oscillator can beadjusted to have substantially less degradation in said compensatedtemperature range by varying load capacitance.
 2. A multi-crystaloscillator for self temperature compensation as Claimed in claim 1,wherein the effective equivalent inductance value of the oscillatorelements may be varied by connecting an element in series having aconsiderably high reactance value.
 3. A multi-crystal oscillator asclaimed in claim 1, characterized in that the oscillator comprisesfigure of merit Psi and degradation factor phi in the following range:20 < Psi < 1,000 -0.05 < phi < 0.05 wherein, the figure of merit Psi isgiven by, Psi ( Delta T)2/ Delta D and the degradation factor phi isgiven by, phi Dc''-Dc/Da''-Da- 1 wherein, Delta D represents variationof normalized frequency deviation at a frequency temperaturecharacteristic having two minimum points of equal oscillation frequencyand Delta D is difference of normalized frequency deviation between theminimum frequency point and most deviated frequency point in a desiredcompensated temperature range, Delta T is a normalized compensationtemperature range corresponding to half of the desired compensatedtemperature range, Da and Dc are normalized frequency deviations of thetwo minimum points having identical value at the equal ripplecharacteristics, Da'' and Dc'' are normalized frequency deviations ofcorresponding points with said two points when oscillation frequency ofthe oscillator is adjusted.